Angles between 0 and 360 degrees IB Studies

Angles between 0 and 360 degrees IB Studies www. ibmaths. com

Investigating angles Ensure that your calculator is in degree mode and write down each of the following to 3 significant figures. sin 30 sin 100 tan 30 cos 30 sin 80 tan 70 cos 280 tan 210 cos 330 cos 60 sin 50 tan 185 sin 130 tan 250 cos 300 tan 5 sin 150 cos 80 Write down the answers which are the same in pairs: E. g. sin 30=sin 150 Can you find a rule based on your findings: sin a = sin ___ tan a = tan ___ cos a = cos ___

Investigating angles - answers sin 30=sin 150 The Rules: sin 50=sin 130 sin 80=sin 100 sin a = sin (180 -a) tan 30=tan 210 tan 70=tan 250 tan a = tan (180+a) tan 5=tan 185 cos 30=cos 330 cos 60=cos 300 cos 80=cos 280 cos a = cos (360 -a)

Investigating angles - negative answers Ensure that your calculator is in degree mode and write down each of the following to 3 significant figures. Write down the answers which are the same in pairs: E. g. sin 210=sin 330 sin 210 sin 200 tan 150 cos 210 sin 315 tan 100 Can you find a rule based on your findings, this is a bit harder. cos 120 tan 330 cos 150 sin (180+a) = sin ___ cos 170 sin 225 tan 280 sin 340 tan 175 tan 355 sin 330 cos 240 cos 190 tan (180 -a) = tan ___ cos (180 -a) = cos ___

Investigating angles - negative answers sin 210=sin 330 The Rules: sin 200=sin 340 sin 225=sin 315 sin (180+a) = sin (360 -a) tan 150=tan 330 tan 100=tan 280 tan (180 -a) = tan (360 -a) tan 175=tan 355 cos 150=cos 210 cos 120=cos 240 cos 170=cos 190 cos (180 -a) = cos (180+a)

Why? - The sine graph 2 answers 30 o and 150 o 2 answers 210 o and 330 o

Why? - The cosine graph 2 answers 60 o and 300 o 2 answers 120 o and 240 o

Why? - The tangent graph 2 answers 45 o and 225 o 2 answers 135 o and 315 o

The CAST diagram 90 o to 180 o All Sin+ Cos+ Tan+ Sin+ Cos. Tan- Tan Sino o 180 to 270 Cos. Tan+ o 0 to o 90 0 o o 360 Cos Sin- 270 o to 360 o Cos+ Tan 270 o CAST

Answering questions 1 - positives Just remember the different rules that apply for tan and cos.

Answering questions 2 - negatives

Questions 1. Find the values of the letters in the following. All the letters are between 0 and 360. 2. Find 2 values for the letters in each of the following. All the letters are between 0 and 360. a) sin 40=sin a a=140 a) sina=0. 906 b) tan 120=tan b b=300 b) cosb=-0. 819 c) cos 52=cos c c=308 c) tanc=1. 43 c=55, 235 d) tan 25=sin d d=205 d) cosd=0. 423 d=65, 295 e) sin 203=sin e e=337 e) tane=-0. 364 e=200, 340 f) cos 230=cos f f=130 f) sinf =-0. 996 f=265, 275 a=65, 115 b=145, 225